Since you are the noncustodial parent claiming the exemption, you need to enter under 6 months for how many months of the year your children lived with you.
The other parent qualifies for tax benefits as well. The tax benefits for custodial parents not claiming dependents are based on the children living with the custodial parents for more than half of the year.
The custodial parent can use the head of household filing status, and the can claim the earned income credit, and the child and dependent care credit.
The noncustodial parent can claim the exemption deduction and the child tax credit.